SSC CGL 2021 PYQ — Question 67

SSC CGL - 18 Aug 2021 - Shift 2 • Quantitative Aptitude • Q67

What is the length (in cm) of the smallest altitude of the trinagle whose sides are 5 cm, 12 cm and 13 cm? (correct to one decimal place)

Show answer & explanation

Correct answer: D

Explanation

The correct answer is option 4 i.e. 4.6

The sides of the triangle are 5, 12 and 13.

Area of triangle = s(s−a)(s−b)(s−c)\sqrt{s(s-a)(s-b)(s-c)} , where s = 15

= 15(15−5)(15−12)(15−13)\sqrt{15(15-5)(15-12)(15-13)}

= 5 × 3 × 2

= 30 cm2.

As one knows the base and their corresponding height is inversely proportional.

⇒ 30 = 1/2 × 13 × h

⇒ h = 4.6.